In the
talk, I will introduce the curve counting theory via ideal sheaves/stable pairs
on 'Calabi-Yau' threefold. According to Diaconescu’s work, the moduli of stable
ADHM quiver bundles on a smooth projec- tive curve X is naturally isomorphic to
the moduli of stable pairs on C2 × X. We extend this with Γ-action on C2, where
Γ is a finite subgroup of SL2(C). Using McKay correspondence, certain stable
pairs on Γ- Hilb(C2)×X relate to stable ADE quiver bundles which correspond to
stable quasimaps.